Thus far we said an individual allocates their time between work and
Leisure. However, we know when people are home they are often
performing household work. We want to expand our model and say
that people allocate their time between work and producing things in
the home. For example, child rearing and household preparation of
food, cleaning etc. Additionally the amount of labor we are
willing to supply also depends on what other household members are
doing. For example, if a member of your household supplies labor
and earns $150,000 per year that may influence you not to supply labor,
but that does not mean you are staying home consuming leisure.
You may be spending your time raising children and managing the
household. So all household members (notice a household can be as
traditional as a husband and wife or as untraditional as we like)
derive joint utility from each other. Also many commodities
consumed by the household are produced or can be produced at home. Thus
a household member who stays home may be engaged in production rather
than just the consumption of leisure.
The new model of labor supply will examine the alternative to work at
household production rather than leisure. Interestingly, the results
about the supply of labor will be the same as in chapter 6.
Household time is an input in household production. Consumption of those goods produced at home provides utility.
We assume that an individual must choose between working for pay and working at home.
Assume we are talking about a single father with a child who gets
satisfaction from raising his child. How much time will he spend on
household work? As before we assume there are 16 available hours
to be divided between paid work, leisure, or household work. Figure 7.1
Time is on the horizontal axis with Household time and time at paid
work. Income is on the vertical axis like before. The father wants to
maximize utility and can do so by buying commodities that increase his
utility (clean house, good food, happy kids, fun life) by either
spending time in household production to make all these things giving
him utility happen or by earning income that allows him to buy goods
and services from others.
His choices are affected by his preferences, his income and his wage rate.
The indifference curve is downward sloping which represents his
preferences. He wants to maximize utility for himself by allocating his
time between working for pay and working at home.
Since different combinations of household time and purchased goods or
services potentially generate equal satisfaction we can use
indifference curves to represent all the time/good combinations that
produce equal utility for the single father. The further from the
origin is the indifference curve the more utility received.
Again on any given indifference curve utility is constant.
Remember if household production increases, hours worked declines and visa versa. What does the negative slope tell us?
What does the convexity of the indifference curve tell us?
As we spend less time in household production (moving up the vertical
part) it becomes more difficult to make up for that special time with
bought goods and services. That is why the slope gets steeper; we
have to pay more and more in terms of bought household goods to make up
for the time not producing household goods since we are spending so
little time to start off with. Now if we are spending a lot of
time on household production, to give up some of that time we do not
have to hire many people. That is, if you spend 12 hours a day on
household production it is easier to spend a little less time by buying
goods instead of producing them yourself. You have lots of time to give
up by working. This is why baby sitters earn very little.
You have lots of time so to get one night out you will hire a baby
sitter but will not spend much. After all, you don't need a
highly trained person to care for your child on a Saturday night; you
just need someone to watch them. But if you spend very little
time in household production initially then to reduce that small amount
of time you spend with your child means you will need trained
professional to make up for your time, thus will have to pay them
more. Thus the slope is steeper when you spend little time in
household production and flatter when you spending lots of time.
Remember if utility is constant, and there is a small amount household
time to begin with, a further reduction may be hard to do while keeping
utility constant. Thus if the single father is traveling weeks at
a time for his job (he has little time to spend with his child) he will
need to pay an expensive nanny who has the training to bring up a
child. Or have the child attend an expensive boarding school as
the child gets older. On the other hand if he spends a lot of
time in household production it will be easy to replace some of that
time with purchased goods (the cheaper babysitter just has to watch the
kid not raise him). But as your have less time for household
production your must purchase more high valued goods.
The slope shows the trade off between household time and purchased
goods or services in the production of household commodities such as
child rearing, or cooking or what ever is produced at home.
If the indifference curve is steep it is difficult to substitute
purchased goods for the loss of an hour of household time, thus must
give up a lot of purchased good. If the indifference curve is
flat then it is easier to substitute purchased goods for household
time.
Notice, since there are only two uses of time (work or household
production) deciding the utility maximizing mode of child-rearing is
the same as deciding the utility maximizing supply of labor.
First to maximize utility we must introduce the budget constraint line
CBA. In 7.1 she earns $10 an hour and has $20 of unearned income. So
her budget constraint is $180. Just as before, the budget
constraint shows different combination of purchases and household time
that are possible for the individual. The slope of budget line, as
before, is the wage rate. (It tells us the increased value of
purchases made possible by an additional hour of paid work) The point
of tangency tells us the utility maximizing point. This tangency
point gives us the number of hours spent in household production and
the value of goods bought. Notice once the number of hours spent
in household production is determined, then we know the number of hours
of labor supplied.
How do we know this?
As in chapter 6 there is an income effect and a substitution
effect. We do not know which effects dominates in advance but if
wages rise and the supply curve is positive then the substitution
effect dominates. And if supply is negative when wages rise then the
income effect dominates.
Notice if the indifference curve is steep it is more difficult to
substitute purchased goods for household production. That is it
is very expensive thus you spend more time in household production and
supply less labor. If the isoquant is flatter then it is easier
to substitute purchased goods for an hour of time and the utility
maximizing point of tangency would show less household production and
more hours worked.
If non-wage income rises for our father his budget line shifts out and
he would receive more utility. The reason he gets more utility is
that he now spends more time in household production with his child
(remember joint utility with child) and supplies less labor. Thus we
see the income effect. Notice exact same income effect as in
chapter six. When income rises he spends more time in household
production with his child and thus works less hours. (In chapter
6 when income rose he bought more leisure and worked fewer hours)
While the income effect tells us the father will spend less time in the
paid labor market the substitution effect tells us he will spend less
time in household production (because cost more when wages rise) thus
he will work more hours.
Thus even though this model emphasizes household production rather than
leisure, the conclusion is the same about how much labor we
supply. This model does however give us a deeper understanding
about how an individual determines how much labor they will supply in
the paid labor market.
Our model is now expanded in that now we can take into consideration
three ways in which people spend their time. Market work (earning
income) household work and leisure activities.
Chapter 6 indicated that the substitution effect tends to dominate for
women. Thus when their wages rise they tend to supply more labor
and buy less leisure. One reason for this is that for women
in the early 1960’s and 1970’s they had low labor force
participation rates and thus spent a lot of time not in the paid labor
market. Usually they didn't just consume leisure but spent time
in household production. When their labor force participation rates
started to rise they had less time in non paid hours including
household production thus they had less time to give up when wages
increased. Consequently we start to see a supply curve for labor that
resembles males.
Men on the other hand tend to have the income effect dominate.
Since they spend very little time in household production to start off
with when their wages increased the income effect tended to
dominate, i.e. wages went up they worked less because they bought more
leisure.
The difference between men and women with respect to the substitution effect can also be explained by the following.
Since their is a substitution effect for household production and
leisure we note that men for reasons of traditional and social and
cultural mores tend not to partake much in household production.
Men traditionally worked and did not stay at home. This work
experience raises their productivity for working thus allowing them to
command a greater income. Men specialized in working in the paid
labor market.
Women by tradition tended to participate in household production.
They were relatively more productive than men because historically they
provided these tasks. If they were so productive at home they did
not have the skills to earn a higher wage in the paid labor
market. Thus their time especially when young children were
around was worth more in household production than in the paid labor
market. As social conditions changed and more women entered the
labor market they became more productive and earned more income.
Government also made it illegal to discriminate against women. We
notice that when wages rise for women the substitution effect between
market and household-work is stronger than men. Thus when wages rise
women tend to substitute goods for hours spent in household
production. Thus they spend less time in household work and
supply more labor when wages rise. (Substitute work for household
production) Also as wages rise women buy less leisure because it
is more expensive and work more hours. Thus we see for females
there are two substitution effects which have them working more hours
when wages rise.
Men on the other hand do not provide as much household production
so when their wages rise they have the substitution effect for leisure
but not for household production. So they have a bigger income
effect and as wages rise for men they work less. Women on the
other hand have two substitution effects thus when wages rise they tend
to work more to make up for household production which they now
purchase.
Now as women’s LFPR increase they have less time to give
up in household production thus they work more hours and start
converging to men in hours worked.
Joint decision to supply labor
The decision to supply ones own labor is jointly determined by what
other members of the household are doing. Their is a joint
decisions that affect the labor supply.
Partners tend to specialize between household and market work.
How do partners determine who specializes in what. Who will be
the primary care giver of children is often a major joint labor
decision. This will depend on who is relatively more productive
at home and who is more productive at work. Who is more
productive at home depends upon who can produce more commodities (hence
more utility) at home. Who’s is more productive at work
depends upon who can generate more income which will allow them to buy
more goods for every extra hour worked.
Who stays at home depends on how much you forfeit in pay, and how
productive you are at child rearing. As we just mentioned females
traditionally do child rearing due to socialization, thus females tend
to be more productive in household production than men. Since
they do not have the market experience nor the training females earn
less than men. Thus their opportunity cost are lower.
Consequently they specialized in household production and child
rearing. However, as wages change for women they must forfeit
more and more goods to stay home, thus they will spend less time in
child rearing. (there opportunity costs are rising) As more women
work and gain experience and become more productive in the paid labor
market they earn more. While they are working men are doing more
child rearing and becoming more productive at household production
(more experience makes you more productive). Thus the shift of
specialization is starting to change. If partners are substitutes
for each other in household production if one increases labor supply
the other will decrease labor supply. If on the other hand the
two are complements in the consumption of household goods, then if one
increases supply of labor the other will do the same. Theory can
not predict if people are substitutes or complements in household
production.
Discouraged and Added worker hypothesis
Suppose males work in the paid labor market and females engages in
household production. Also suppose there is a recession and the
male becomes unemployed. His market productivity declines
relative to his household productivity (which does not decline at all
as a result of the recession.) Thus the family may benefit by him
engaging in household production. In order for the family to
maintain same utility the spouse of the unemployed partner may enter
the labor market to generate income to offset what the unemployed
partner is loosing. Thus the husband stays home and engages in
household production. Thus during a recession a worker is added
to the labor market. This was very valid when LFPR rates were low
for women. But now since LFPR are higher not sure if it is as
valid. This is like an income effect because as income falls more
people in the family seek market work. If seeking market work
less time is spent in consumption as income declines, thus an income
effect. Sometimes when women become an added workers and do not
get a job the unemployment rate gets even higher because now two people
are out of work because the added worker could not find a job.
There is also what is called a discouraged worker effect.
As wages fall due to unemployment the husband gets discouraged and
stops looking for work. This is usually after a long period of
not finding a job. Basically people feel that it is a waste of
time looking for work, and it would be better for them to spend time in
household production. Thus because of high unemployment during a
recession, real wages decline and a person expected wage fall thus give
up looking for work. Supply of labor declines and hours in
household production increases. This is the substitution
effect. (Notice opposite of the substitution effect when we
discussed it for wages rising) now wages are falling.
Thus the substitution effect of the discouraged worker offsets the
income effect of the added worker. Which one is stronger is an
empirical question. The added worker effect tends to be
small. The discouraged worker effect tends to dominate.
This leads to hidden unemployment, because when out of the labor force
no longer considered unemployed. Hidden unemployment can boost
unemployment by as much at 2%.
Life-Cycle Aspects of Labor Supply
People will vary the amount of labor they supply over different points
of time in their life cycle. Thus we can add another dimension to
the supply of labor by looking at how LFPR differ at different points
in a person’s life-cycle. For example 18 year olds have a
low opportunity cost so it pays for them to get an education and not be
in the labor force. When a family has young children one member
of the family might be relatively more productive in household
production thus will not supply labor. Since their indifference
curve is steep (showing they would need a lot of money to make up for
reduced time in household production) they tend to spend more time in
household production. Since this is often the mother we see
mothers of young children spend more time in household production than
in the paid labor market.
Also as we age we often slow down and become less productive in the
paid labor market, thus it may pay for us to retire because our
opportunity costs are being reduced.
Thus we see that the supply of labor varies as we enter and exit different stages in our lives.